Vectors & Scalars
- Scalars are fully defined by magnitude only
- Distance - this is the distance travelled from A to B
- Vectors have a magnitude and direction
- May put arrow on top to indicate $\vec{s}$
- Exceptions do exist if the question asks for the magnitude (understand context of question)
- Also, if given compass directions, then return in compass directions.
- Don't write compass directions if they are not explicitly given; for rivers, for example, just write up/downstream if North not given
- Assume vehicles are moving forward
- Assume falling objects are going down
- Below is a vector quantity table;
| Vector | Symbol | Scalar | Units |
|---|
| Displacement | $s$ | Distance | $m$ |
| Velocity | $v$ ($=\frac{s}{t}$) | Speed | $m s^{-1}$ |
| Acceleration | $a$ ($=\frac{v}{t}$) | | $ms^{-2}$ |
| Force | $F$ ($=ma$) | | $N$ |
| $W$ ($=F_s$) | Work | $J$ |
| | Mass | $KG$ |
| | Temperature | $C$ or $K$ |
Vector vs Free body diagram
- Free body diagrams show all real forces acting on a body
- $W$ - weight/gravitational force
- $Lift$ - lift force
- $Drag$ - drag force
- $Thrust$ - thrust force
- Don't write acceleration - it isn't a force!
- The diagram is centered on a dot
- Vector diagrams show the resolved vectors acting in a situation
- Must use arrows (same for FBD)
- Must have the same vector quantity on each side
- Must be resolved
- Define own compass direction (for relevant questions)
- Head to Tail